व्यंजक (4(3x-2)-5(x+1)) का सरल रूप क्या है?
What is the simplified form of (4(3x-2)-5(x+1))?
#algebraic_expressions
#hard
#expansion
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A (7x-13)
B (17x-3)
C (7x+13)
D (17x-13)
Explanation opens after your attempt
Correct Answer
A. (7x-13)
Step 1
Concept
Expanding gives (12x-8-5x-5=7x-13). Expand first and then combine like terms.
Step 2
Why this answer is correct
The correct answer is A. (7x-13). Expanding gives (12x-8-5x-5=7x-13). Expand first and then combine like terms.
Step 3
Exam Tip
कोष्ठक खोलने पर (12x-8-5x-5=7x-13) मिलता है। पहले विस्तार करें फिर समान पद जोड़ें।
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यदि (x=-3), तो \(2x^2+5x-4\) का मान क्या होगा?
If (x=-3), what is the value of \(2x^2+5x-4\)?
#algebraic_expressions
#hard
#evaluation
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A (-1)
B (1)
C (29)
D (17)
Explanation opens after your attempt
Step 1
Concept
Substitution gives (2(9)-15-4=-1). The square of a negative number is positive.
Step 2
Why this answer is correct
The correct answer is A. (-1). Substitution gives (2(9)-15-4=-1). The square of a negative number is positive.
Step 3
Exam Tip
मान रखने पर (2(9)-15-4=-1) मिलता है। ऋणात्मक संख्या का वर्ग धनात्मक होता है।
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व्यंजक \(6a^2-4a+9-2a^2+7a-5\) का सरल रूप क्या है?
What is the simplified form of \(6a^2-4a+9-2a^2+7a-5\)?
#algebraic_expressions
#hard
#like_terms
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A \(8a^2+3a+4\)
B \(4a^2+3a+4\)
C \(4a^2-11a+14\)
D \(8a^2-11a+4\)
Explanation opens after your attempt
Correct Answer
B. \(4a^2+3a+4\)
Step 1
Concept
Combining like terms gives \(6a^2-2a^2=4a^2\), (-4a+7a=3a), and (9-5=4). Group terms by powers.
Step 2
Why this answer is correct
The correct answer is B. \(4a^2+3a+4\). Combining like terms gives \(6a^2-2a^2=4a^2\), (-4a+7a=3a), and (9-5=4). Group terms by powers.
Step 3
Exam Tip
समान पद जोड़ने पर \(6a^2-2a^2=4a^2\), (-4a+7a=3a), और (9-5=4) मिलता है। घात के अनुसार पद समूहित करें।
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(8x-3) में से (2x+7) घटाने पर क्या मिलेगा?
What is obtained by subtracting (2x+7) from (8x-3)?
#algebraic_expressions
#hard
#subtraction
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A (10x+4)
B (6x+4)
C (6x-10)
D (10x-10)
Explanation opens after your attempt
Correct Answer
C. (6x-10)
Step 1
Concept
((8x-3)-(2x+7)=8x-3-2x-7=6x-10). Change signs of both terms of the subtracted expression.
Step 2
Why this answer is correct
The correct answer is C. (6x-10). ((8x-3)-(2x+7)=8x-3-2x-7=6x-10). Change signs of both terms of the subtracted expression.
Step 3
Exam Tip
((8x-3)-(2x+7)=8x-3-2x-7=6x-10)। घटाए गए व्यंजक के दोनों पदों के चिह्न बदलें।
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यदि (x=2) और (y=-4), तो \(3x^2-2xy+y\) का मान क्या होगा?
If (x=2) and (y=-4), what is the value of \(3x^2-2xy+y\)?
#algebraic_expressions
#hard
#two_variable_evaluation
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A (16)
B (20)
C (24)
D (28)
Explanation opens after your attempt
Step 1
Concept
Substitution gives (3(4)-2(2)(-4)-4=24). Keep signs carefully in two-variable questions.
Step 2
Why this answer is correct
The correct answer is C. (24). Substitution gives (3(4)-2(2)(-4)-4=24). Keep signs carefully in two-variable questions.
Step 3
Exam Tip
मान रखने पर (3(4)-2(2)(-4)-4=24) मिलता है। दो चर वाले प्रश्न में चिह्न ध्यान से रखें।
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व्यंजक (5(2m-3n)-2(m+n)) का सरल रूप क्या है?
What is the simplified form of (5(2m-3n)-2(m+n))?
#algebraic_expressions
#hard
#two_variable
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A (8m-17n)
B (8m-13n)
C (12m-17n)
D (12m-13n)
Explanation opens after your attempt
Correct Answer
A. (8m-17n)
Step 1
Concept
Expanding gives (10m-15n-2m-2n=8m-17n). Combine (m) and (n) terms separately.
Step 2
Why this answer is correct
The correct answer is A. (8m-17n). Expanding gives (10m-15n-2m-2n=8m-17n). Combine (m) and (n) terms separately.
Step 3
Exam Tip
खोलने पर (10m-15n-2m-2n=8m-17n) मिलता है। (m) और (n) के पद अलग-अलग जोड़ें।
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कौन सा व्यंजक (p) और (3) के योग के (4) गुने में से (p) घटाने को दर्शाता है?
Which expression represents subtracting (p) from (4) times the sum of (p) and (3)?
#algebraic_expressions
#hard
#word_expression
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A (4p+3-p)
B (4(p+3)-p)
C (p-4(p+3))
D (4(p-3)+p)
Explanation opens after your attempt
Correct Answer
B. (4(p+3)-p)
Step 1
Concept
First the sum is (p+3), and four times it is (4(p+3)). Then (p) is subtracted from it.
Step 2
Why this answer is correct
The correct answer is B. (4(p+3)-p). First the sum is (p+3), and four times it is (4(p+3)). Then (p) is subtracted from it.
Step 3
Exam Tip
पहले योग (p+3) है और उसका (4) गुना (4(p+3)) है। फिर उसमें से (p) घटता है।
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यदि (r=-2), तो \(r^3-4r^2+6r\) का मान क्या होगा?
If (r=-2), what is the value of \(r^3-4r^2+6r\)?
#algebraic_expressions
#hard
#cubic_evaluation
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A (-20)
B (-24)
C (-36)
D (-12)
Explanation opens after your attempt
Step 1
Concept
Substitution gives (-8-16-12=-36). Even and odd powers have different sign behavior.
Step 2
Why this answer is correct
The correct answer is C. (-36). Substitution gives (-8-16-12=-36). Even and odd powers have different sign behavior.
Step 3
Exam Tip
मान रखने पर (-8-16-12=-36) मिलता है। सम और विषम घातों के चिह्न अलग होते हैं।
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व्यंजक (3x-[4x-{2x-5}]) का सरल रूप क्या है?
What is the simplified form of (3x-[4x-{2x-5}])?
#algebraic_expressions
#hard
#nested_brackets
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A (x+5)
B (x-5)
C (5x+5)
D (5x-5)
Explanation opens after your attempt
Step 1
Concept
Inside (4x-(2x-5)=2x+5), then (3x-(2x+5)=x-5). Handle brackets carefully.
Step 2
Why this answer is correct
The correct answer is A. (x+5). Inside (4x-(2x-5)=2x+5), then (3x-(2x+5)=x-5). Handle brackets carefully.
Step 3
Exam Tip
अंदर (4x-(2x-5)=2x+5), फिर (3x-(2x+5)=x-5) नहीं बल्कि (x-5) मिलता है। कोष्ठक सावधानी से खोलें।
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व्यंजक (3x-[4x-{2x-5}]) का सही सरल रूप कौन सा है?
Which is the correct simplified form of (3x-[4x-{2x-5}])?
#algebraic_expressions
#hard
#braces
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A (x+5)
B (x-5)
C (5x-5)
D (5x+5)
Explanation opens after your attempt
Step 1
Concept
Inside (4x-{2x-5}=2x+5). Therefore (3x-(2x+5)=x-5).
Step 2
Why this answer is correct
The correct answer is B. (x-5). Inside (4x-{2x-5}=2x+5). Therefore (3x-(2x+5)=x-5).
Step 3
Exam Tip
अंदर (4x-{2x-5}=2x+5) है। इसलिए (3x-(2x+5)=x-5)।
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किस विकल्प में (7ab-4a+3ab+9a) का सही सरल रूप है?
Which option gives the correct simplified form of (7ab-4a+3ab+9a)?
#algebraic_expressions
#hard
#multivariable_terms
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A (10ab+5a)
B \(10a^2b+5a\)
C (4ab+13a)
D (10ab-13a)
Explanation opens after your attempt
Correct Answer
A. (10ab+5a)
Step 1
Concept
(7ab+3ab=10ab) and (-4a+9a=5a). (ab) and (a) are unlike terms.
Step 2
Why this answer is correct
The correct answer is A. (10ab+5a). (7ab+3ab=10ab) and (-4a+9a=5a). (ab) and (a) are unlike terms.
Step 3
Exam Tip
(7ab+3ab=10ab) और (-4a+9a=5a)। (ab) और (a) असमान पद हैं।
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यदि (a+b=9) और (ab=14), तो (3(a+b)-2ab) का मान क्या होगा?
If (a+b=9) and (ab=14), what is the value of (3(a+b)-2ab)?
#algebraic_expressions
#hard
#given_values
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A (-1)
B (1)
C (13)
D (41)
Explanation opens after your attempt
Step 1
Concept
Using the given values gives (3(9)-2(14)=27-28=-1). Treat the whole (a+b) as one value.
Step 2
Why this answer is correct
The correct answer is A. (-1). Using the given values gives (3(9)-2(14)=27-28=-1). Treat the whole (a+b) as one value.
Step 3
Exam Tip
दिए गए मान रखने पर (3(9)-2(14)=27-28=-1) मिलता है। पूरे (a+b) को एक मान की तरह लें।
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व्यंजक (2x(5x-3)-3x(2x+1)) का सरल रूप क्या है?
What is the simplified form of (2x(5x-3)-3x(2x+1))?
#algebraic_expressions
#hard
#product_expansion
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A \(4x^2-9x\)
B \(16x^2-3x\)
C \(4x^2+9x\)
D \(16x^2-9x\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-9x\)
Step 1
Concept
Expanding gives \(10x^2-6x-6x^2-3x=4x^2-9x\). Do each multiplication separately.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-9x\). Expanding gives \(10x^2-6x-6x^2-3x=4x^2-9x\). Do each multiplication separately.
Step 3
Exam Tip
खोलने पर \(10x^2-6x-6x^2-3x=4x^2-9x\) मिलता है। हर गुणन को अलग से करें।
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किस विकल्प में \(-3x^2\) और \(8x^2\) का अंतर \(-3x^2-8x^2\) सही है?
Which option gives the correct difference \(-3x^2-8x^2\)?
#algebraic_expressions
#hard
#subtract_like_terms
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A \(-11x^2\)
B \(5x^2\)
C \(-5x^2\)
D \(-11x^4\)
Explanation opens after your attempt
Correct Answer
A. \(-11x^2\)
Step 1
Concept
The coefficients of like terms are (-3-8=-11). The variable part \(x^2\) remains the same.
Step 2
Why this answer is correct
The correct answer is A. \(-11x^2\). The coefficients of like terms are (-3-8=-11). The variable part \(x^2\) remains the same.
Step 3
Exam Tip
समान पदों के गुणांक (-3-8=-11) हैं। चर भाग \(x^2\) वही रहता है।
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यदि (x=4), तो \(\frac{x^2+2x-8}{4}\) का मान क्या होगा?
If (x=4), what is the value of \(\frac{x^2+2x-8}{4}\)?
#algebraic_expressions
#hard
#fraction_evaluation
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A (4)
B (5)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
Substitution gives \(\frac{16+8-8}{4}=\frac{16}{4}=4\). Simplify the whole numerator first.
Step 2
Why this answer is correct
The correct answer is A. (4). Substitution gives \(\frac{16+8-8}{4}=\frac{16}{4}=4\). Simplify the whole numerator first.
Step 3
Exam Tip
मान रखने पर \(\frac{16+8-8}{4}=\frac{16}{4}=4\) मिलता है। पहले पूरा अंश सरल करें।
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व्यंजक (9-(2x-3)+4(x-1)) का सरल रूप क्या है?
What is the simplified form of (9-(2x-3)+4(x-1))?
#algebraic_expressions
#hard
#signs
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A (2x+8)
B (2x+14)
C (6x+8)
D (6x-14)
Explanation opens after your attempt
Step 1
Concept
Expanding gives (9-2x+3+4x-4=2x+8). If a minus is outside the bracket, change signs.
Step 2
Why this answer is correct
The correct answer is A. (2x+8). Expanding gives (9-2x+3+4x-4=2x+8). If a minus is outside the bracket, change signs.
Step 3
Exam Tip
खोलने पर (9-2x+3+4x-4=2x+8) मिलता है। कोष्ठक के बाहर ऋण हो तो चिह्न बदलें।
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एक त्रिभुज की भुजाएं (2x+1), (x+6) और (3x-4) हैं। परिमाप का व्यंजक क्या होगा?
The sides of a triangle are (2x+1), (x+6), and (3x-4). What is the expression for its perimeter?
#algebraic_expressions
#hard
#perimeter
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A (5x+3)
B (6x+3)
C (6x+11)
D (5x+11)
Explanation opens after your attempt
Step 1
Concept
Perimeter is the sum of all sides. ((2x+1)+(x+6)+(3x-4)=6x+3).
Step 2
Why this answer is correct
The correct answer is B. (6x+3). Perimeter is the sum of all sides. ((2x+1)+(x+6)+(3x-4)=6x+3).
Step 3
Exam Tip
परिमाप सभी भुजाओं का योग है। ((2x+1)+(x+6)+(3x-4)=6x+3)।
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व्यंजक (4p-[2p-{3p-(p-2)}]) का सरल रूप क्या है?
What is the simplified form of (4p-[2p-{3p-(p-2)}])?
#algebraic_expressions
#hard
#nested_simplification
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A (4p+2)
B (4p-2)
C (2p+2)
D (2p-2)
Explanation opens after your attempt
Step 1
Concept
Inside (3p-(p-2)=2p+2), then (2p-(2p+2)=-2), so (4p-(-2)=4p+2). Simplify from inside to outside.
Step 2
Why this answer is correct
The correct answer is A. (4p+2). Inside (3p-(p-2)=2p+2), then (2p-(2p+2)=-2), so (4p-(-2)=4p+2). Simplify from inside to outside.
Step 3
Exam Tip
अंदर (3p-(p-2)=2p+2), फिर (2p-(2p+2)=-2), इसलिए (4p-(-2)=4p+2)। अंदर से बाहर की ओर सरल करें।
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यदि (u=-1) और (v=3), तो \(u^2v-uv^2+2u\) का मान क्या होगा?
If (u=-1) and (v=3), what is the value of \(u^2v-uv^2+2u\)?
#algebraic_expressions
#hard
#two_variable_power
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A (8)
B (10)
C (12)
D (14)
Explanation opens after your attempt
Step 1
Concept
Substitution gives (1(3)-(-1)(9)+2(-1)=10). Find the sign of \(uv^2\) carefully.
Step 2
Why this answer is correct
The correct answer is B. (10). Substitution gives (1(3)-(-1)(9)+2(-1)=10). Find the sign of \(uv^2\) carefully.
Step 3
Exam Tip
मान रखने पर (1(3)-(-1)(9)+2(-1)=10) मिलता है। \(uv^2\) के चिह्न को सावधानी से निकालें।
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कौन सा व्यंजक (x) से (4) कम संख्या के वर्ग को दर्शाता है?
Which expression represents the square of the number (4) less than (x)?
#algebraic_expressions
#hard
#word_to_expression
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A \(x^2-4\)
B \(x-4^2\)
C ((x-4)2 )
D \(4-x^2\)
Explanation opens after your attempt
Correct Answer
C. ((x-4)2 )
Step 1
Concept
The number (4) less than (x) is (x-4). To square the whole difference, write ((x-4)2 ).
Step 2
Why this answer is correct
The correct answer is C. ((x-4)2 ). The number (4) less than (x) is (x-4). To square the whole difference, write ((x-4)2 ).
Step 3
Exam Tip
(4) कम संख्या (x-4) है। पूरे अंतर के वर्ग के लिए ((x-4)2 ) लिखते हैं।
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व्यंजक \(7x^2-2xy+5xy-3x^2\) का सरल रूप क्या है?
What is the simplified form of \(7x^2-2xy+5xy-3x^2\)?
#algebraic_expressions
#hard
#combine_terms
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A \(4x^2+3xy\)
B \(10x^2+3xy\)
C \(4x^2-7xy\)
D \(10x^2-7xy\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2+3xy\)
Step 1
Concept
\(7x^2-3x^2=4x^2\) and (-2xy+5xy=3xy). \(x^2\) and (xy) are different variable parts.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2+3xy\). \(7x^2-3x^2=4x^2\) and (-2xy+5xy=3xy). \(x^2\) and (xy) are different variable parts.
Step 3
Exam Tip
\(7x^2-3x^2=4x^2\) और (-2xy+5xy=3xy)। \(x^2\) और (xy) अलग चर भाग हैं।
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यदि (x-y=8), तो (5x-5y-6) का मान क्या होगा?
If (x-y=8), what is the value of (5x-5y-6)?
#algebraic_expressions
#hard
#given_difference
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A (34)
B (40)
C (46)
D (14)
Explanation opens after your attempt
Step 1
Concept
(5x-5y-6=5(x-y)-6=5(8)-6=34). If coefficients are same, take the common factor.
Step 2
Why this answer is correct
The correct answer is A. (34). (5x-5y-6=5(x-y)-6=5(8)-6=34). If coefficients are same, take the common factor.
Step 3
Exam Tip
(5x-5y-6=5(x-y)-6=5(8)-6=34)। समान गुणांक हो तो सामान्य गुणक निकालें।
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व्यंजक (3(2x-y)-2(x-3y)+4y) का सरल रूप क्या है?
What is the simplified form of (3(2x-y)-2(x-3y)+4y)?
#algebraic_expressions
#hard
#linear_combination
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A (4x+7y)
B (4x+13y)
C (8x+7y)
D (8x+13y)
Explanation opens after your attempt
Correct Answer
A. (4x+7y)
Step 1
Concept
Expanding gives (6x-3y-2x+6y+4y=4x+7y). Combine terms with the same variable.
Step 2
Why this answer is correct
The correct answer is A. (4x+7y). Expanding gives (6x-3y-2x+6y+4y=4x+7y). Combine terms with the same variable.
Step 3
Exam Tip
खोलने पर (6x-3y-2x+6y+4y=4x+7y) मिलता है। समान चर वाले पद जोड़ें।
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किस विकल्प में \(x^2-3x+2\) और \(2x^2+x-5\) का योग सही है?
Which option gives the correct sum of \(x^2-3x+2\) and \(2x^2+x-5\)?
#algebraic_expressions
#hard
#polynomial_addition
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A \(3x^2-2x-3\)
B \(x^2-4x+7\)
C \(3x^2+2x-3\)
D \(3x^2-4x+7\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-2x-3\)
Step 1
Concept
In the sum, \(x^2+2x^2=3x^2\), (-3x+x=-2x), and (2-5=-3). Add like terms separately.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-2x-3\). In the sum, \(x^2+2x^2=3x^2\), (-3x+x=-2x), and (2-5=-3). Add like terms separately.
Step 3
Exam Tip
योग में \(x^2+2x^2=3x^2\), (-3x+x=-2x), और (2-5=-3) है। समान पदों को अलग-अलग जोड़ें।
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यदि (x=0), तो \(7x^3-5x^2+2x-9\) का मान क्या होगा?
If (x=0), what is the value of \(7x^3-5x^2+2x-9\)?
#algebraic_expressions
#hard
#zero_substitution
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A (0)
B (-9)
C (9)
D (2)
Explanation opens after your attempt
Step 1
Concept
Putting (x=0) makes all variable terms (0). Therefore the value is (-9).
Step 2
Why this answer is correct
The correct answer is B. (-9). Putting (x=0) makes all variable terms (0). Therefore the value is (-9).
Step 3
Exam Tip
(x=0) रखने पर चर वाले सभी पद (0) हो जाते हैं। इसलिए मान (-9) है।
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व्यंजक (2a-3[4a-2(a-5)]) का सरल रूप क्या है?
What is the simplified form of (2a-3[4a-2(a-5)])?
#algebraic_expressions
#hard
#bracket_error
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A (2a-30)
B (-4a-30)
C (-4a+30)
D (2a+30)
Explanation opens after your attempt
Correct Answer
C. (-4a+30)
Step 1
Concept
Inside (4a-2a+10=2a+10), so (2a-3(2a+10)=-4a-30). Keep signs correctly till the end.
Step 2
Why this answer is correct
The correct answer is C. (-4a+30). Inside (4a-2a+10=2a+10), so (2a-3(2a+10)=-4a-30). Keep signs correctly till the end.
Step 3
Exam Tip
अंदर (4a-2a+10=2a+10), इसलिए (2a-3(2a+10)=-4a-30) नहीं बल्कि (-4a-30) है। सही चिह्नों को अंत तक रखें।
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व्यंजक (2a-3[4a-2(a-5)]) का सही सरल रूप कौन सा है?
Which is the correct simplified form of (2a-3[4a-2(a-5)])?
#algebraic_expressions
#hard
#bracket_simplification
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A (2a-30)
B (-4a-30)
C (-4a+30)
D (8a-30)
Explanation opens after your attempt
Correct Answer
B. (-4a-30)
Step 1
Concept
Inside (4a-2(a-5)=2a+10). Therefore (2a-3(2a+10)=-4a-30).
Step 2
Why this answer is correct
The correct answer is B. (-4a-30). Inside (4a-2(a-5)=2a+10). Therefore (2a-3(2a+10)=-4a-30).
Step 3
Exam Tip
अंदर (4a-2(a-5)=2a+10) है। इसलिए (2a-3(2a+10)=-4a-30)।
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यदि (m=3) और (n=-2), तो \(m^2n-mn^2\) का मान क्या होगा?
If (m=3) and (n=-2), what is the value of \(m^2n-mn^2\)?
#algebraic_expressions
#hard
#signed_evaluation
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A (-30)
B (6)
C (-6)
D (30)
Explanation opens after your attempt
Step 1
Concept
Substitution gives (9(-2)-3(4)=-18-12=-30). \(n^2\) will be positive.
Step 2
Why this answer is correct
The correct answer is A. (-30). Substitution gives (9(-2)-3(4)=-18-12=-30). \(n^2\) will be positive.
Step 3
Exam Tip
मान रखने पर (9(-2)-3(4)=-18-12=-30) मिलता है। \(n^2\) धनात्मक होगा।
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किस विकल्प में (5(x+2)-[3x-{x-4}]) का सही सरल रूप है?
Which option gives the correct simplified form of (5(x+2)-[3x-{x-4}])?
#algebraic_expressions
#hard
#mixed_brackets
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A (3x+6)
B (3x+14)
C (7x+6)
D (7x+14)
Explanation opens after your attempt
Step 1
Concept
Inside (3x-(x-4)=2x+4), so (5x+10-(2x+4)=3x+6). Simplify the inner bracket first.
Step 2
Why this answer is correct
The correct answer is A. (3x+6). Inside (3x-(x-4)=2x+4), so (5x+10-(2x+4)=3x+6). Simplify the inner bracket first.
Step 3
Exam Tip
अंदर (3x-(x-4)=2x+4), इसलिए (5x+10-(2x+4)=3x+6)। अंदरूनी कोष्ठक पहले सरल करें।
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(x) से (2) अधिक संख्या और (x) से (3) कम संख्या के योग का व्यंजक क्या होगा?
What is the expression for the sum of the number (2) more than (x) and the number (3) less than (x)?
#algebraic_expressions
#hard
#word_problem
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A (2x-1)
B (2x+5)
C (x-1)
D (x+5)
Explanation opens after your attempt
Step 1
Concept
The two numbers are (x+2) and (x-3). Their sum is (2x-1).
Step 2
Why this answer is correct
The correct answer is A. (2x-1). The two numbers are (x+2) and (x-3). Their sum is (2x-1).
Step 3
Exam Tip
दो संख्याएं (x+2) और (x-3) हैं। उनका योग (2x-1) है।
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व्यंजक \(\frac{5x}{6}-\frac{x}{3}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{5x}{6}-\frac{x}{3}\)?
#algebraic_expressions
#hard
#fraction_terms
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A \(\frac{x}{2}\)
B \(\frac{7x}{6}\)
C \(\frac{4x}{3}\)
D \(\frac{5x^2}{18}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{x}{2}\)
Step 1
Concept
\(\frac{x}{3}=\frac{2x}{6}\), so \(\frac{5x}{6}-\frac{2x}{6}=\frac{x}{2}\). Make common denominators for fraction terms.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{x}{2}\). \(\frac{x}{3}=\frac{2x}{6}\), so \(\frac{5x}{6}-\frac{2x}{6}=\frac{x}{2}\). Make common denominators for fraction terms.
Step 3
Exam Tip
\(\frac{x}{3}=\frac{2x}{6}\), इसलिए \(\frac{5x}{6}-\frac{2x}{6}=\frac{x}{2}\)। भिन्न पदों में समान हर बनाएं।
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यदि (x+y=5) और (x-y=1), तो (2(x+y)+3(x-y)) का मान क्या होगा?
If (x+y=5) and (x-y=1), what is the value of (2(x+y)+3(x-y))?
#algebraic_expressions
#hard
#substitution_given
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A (13)
B (11)
C (10)
D (8)
Explanation opens after your attempt
Step 1
Concept
Using the given values gives (2(5)+3(1)=13). Use the whole bracket as one value.
Step 2
Why this answer is correct
The correct answer is A. (13). Using the given values gives (2(5)+3(1)=13). Use the whole bracket as one value.
Step 3
Exam Tip
दिए गए मान रखने पर (2(5)+3(1)=13) मिलता है। पूरे कोष्ठक को एक मान की तरह उपयोग करें।
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व्यंजक \(6x^2-4xy+2y^2-3x^2+9xy-y^2\) का सरल रूप क्या है?
What is the simplified form of \(6x^2-4xy+2y^2-3x^2+9xy-y^2\)?
#algebraic_expressions
#hard
#quadratic_two_variables
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A \(3x^2+5xy+y^2\)
B \(9x^2+5xy+y^2\)
C \(3x^2-13xy+y^2\)
D \(9x^2+13xy+3y^2\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2+5xy+y^2\)
Step 1
Concept
Combining \(x^2\), (xy), and \(y^2\) terms separately gives \(3x^2+5xy+y^2\). Do not mix different variable parts.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2+5xy+y^2\). Combining \(x^2\), (xy), and \(y^2\) terms separately gives \(3x^2+5xy+y^2\). Do not mix different variable parts.
Step 3
Exam Tip
\(x^2\), (xy), और \(y^2\) पदों को अलग जोड़ने पर \(3x^2+5xy+y^2\) मिलता है। अलग चर भागों को न मिलाएं।
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व्यंजक (10-[3x-2(4-x)]) का सरल रूप क्या है?
What is the simplified form of (10-[3x-2(4-x)])?
#algebraic_expressions
#hard
#square_brackets
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A (18-x)
B (18-5x)
C (2+5x)
D (2+x)
Explanation opens after your attempt
Correct Answer
B. (18-5x)
Step 1
Concept
Inside (3x-8+2x=5x-8), so (10-(5x-8)=18-5x). Apply the outside negative sign carefully.
Step 2
Why this answer is correct
The correct answer is B. (18-5x). Inside (3x-8+2x=5x-8), so (10-(5x-8)=18-5x). Apply the outside negative sign carefully.
Step 3
Exam Tip
अंदर (3x-8+2x=5x-8), इसलिए (10-(5x-8)=18-5x)। वर्ग कोष्ठक के बाहर का ऋण चिह्न ध्यान से लगाएं।
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यदि (t=2), तो \(3t^4-2t^3+t\) का मान क्या होगा?
If (t=2), what is the value of \(3t^4-2t^3+t\)?
#algebraic_expressions
#hard
#power_evaluation
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A (34)
B (36)
C (38)
D (40)
Explanation opens after your attempt
Step 1
Concept
Substitution gives (3(16)-2(8)+2=34). Evaluate higher powers first.
Step 2
Why this answer is correct
The correct answer is A. (34). Substitution gives (3(16)-2(8)+2=34). Evaluate higher powers first.
Step 3
Exam Tip
मान रखने पर (3(16)-2(8)+2=34) मिलता है। बड़ी घातों को पहले निकालें।
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कौन सा व्यंजक (a) और (b) के अंतर के (3) गुने में उनके योग को जोड़ता है?
Which expression adds the sum of (a) and (b) to (3) times their difference?
#algebraic_expressions
#hard
#phrase_expression
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A (3(a-b)+(a+b))
B (3(a+b)+(a-b))
C (3a-b+a+b)
D (a-b+3(a+b))
Explanation opens after your attempt
Correct Answer
A. (3(a-b)+(a+b))
Step 1
Concept
The difference is (a-b), and three times it is (3(a-b)). Adding the sum (a+b) gives (3(a-b)+(a+b)).
Step 2
Why this answer is correct
The correct answer is A. (3(a-b)+(a+b)). The difference is (a-b), and three times it is (3(a-b)). Adding the sum (a+b) gives (3(a-b)+(a+b)).
Step 3
Exam Tip
अंतर (a-b) है और उसका (3) गुना (3(a-b)) है। इसमें योग (a+b) जोड़ने पर (3(a-b)+(a+b)) बनता है।
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व्यंजक ((2x+3)+(4x-7)-(x+5)) का सरल रूप क्या है?
What is the simplified form of ((2x+3)+(4x-7)-(x+5))?
#algebraic_expressions
#hard
#add_subtract_expressions
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A (5x-9)
B (7x+1)
C (5x+1)
D (7x-9)
Explanation opens after your attempt
Step 1
Concept
Removing brackets gives (2x+3+4x-7-x-5=5x-9). Change signs of the subtracted bracket.
Step 2
Why this answer is correct
The correct answer is A. (5x-9). Removing brackets gives (2x+3+4x-7-x-5=5x-9). Change signs of the subtracted bracket.
Step 3
Exam Tip
कोष्ठक हटाने पर (2x+3+4x-7-x-5=5x-9) मिलता है। घटाए गए कोष्ठक के चिह्न बदलें।
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यदि (p=-1), तो \(p^4+2p^3-3p^2+4\) का मान क्या होगा?
If (p=-1), what is the value of \(p^4+2p^3-3p^2+4\)?
#algebraic_expressions
#hard
#negative_one_power
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A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
Substitution gives (1-2-3+4=0). Even powers of (-1) are (1), and odd powers are (-1).
Step 2
Why this answer is correct
The correct answer is A. (0). Substitution gives (1-2-3+4=0). Even powers of (-1) are (1), and odd powers are (-1).
Step 3
Exam Tip
मान रखने पर (1-2-3+4=0) मिलता है। (-1) की सम घात (1) और विषम घात (-1) होती है।
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किस विकल्प में (4x-2y) में से (x+5y) घटाने का सही परिणाम है?
Which option gives the correct result of subtracting (x+5y) from (4x-2y)?
#algebraic_expressions
#hard
#two_variable_subtraction
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A (3x-7y)
B (5x+3y)
C (3x+3y)
D (5x-7y)
Explanation opens after your attempt
Correct Answer
A. (3x-7y)
Step 1
Concept
((4x-2y)-(x+5y)=4x-2y-x-5y=3x-7y). Change signs of the whole second expression while subtracting.
Step 2
Why this answer is correct
The correct answer is A. (3x-7y). ((4x-2y)-(x+5y)=4x-2y-x-5y=3x-7y). Change signs of the whole second expression while subtracting.
Step 3
Exam Tip
((4x-2y)-(x+5y)=4x-2y-x-5y=3x-7y)। घटाते समय पूरे दूसरे व्यंजक के चिह्न बदलें।
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व्यंजक \(3x^2y-5xy^2+7x^2y-2xy^2\) का सरल रूप क्या है?
What is the simplified form of \(3x^2y-5xy^2+7x^2y-2xy^2\)?
#algebraic_expressions
#hard
#multivariable_powers
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A \(10x^2y-7xy^2\)
B \(10x^2y+3xy^2\)
C \(-4x^2y-7xy^2\)
D \(10x^3y^3-7xy^2\)
Explanation opens after your attempt
Correct Answer
A. \(10x^2y-7xy^2\)
Step 1
Concept
\(3x^2y+7x^2y=10x^2y\) and \(-5xy^2-2xy^2=-7xy^2\). Terms are like only when powers match.
Step 2
Why this answer is correct
The correct answer is A. \(10x^2y-7xy^2\). \(3x^2y+7x^2y=10x^2y\) and \(-5xy^2-2xy^2=-7xy^2\). Terms are like only when powers match.
Step 3
Exam Tip
\(3x^2y+7x^2y=10x^2y\) और \(-5xy^2-2xy^2=-7xy^2\)। घातें समान हों तभी पद समान होते हैं।
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यदि (q=3), तो \(\frac{q^3-q}{3}\) का मान क्या होगा?
If (q=3), what is the value of \(\frac{q^3-q}{3}\)?
#algebraic_expressions
#hard
#cubic_fraction
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A (8)
B (6)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
Putting (q=3) gives \(\frac{27-3}{3}=8\). Simplify the numerator completely first.
Step 2
Why this answer is correct
The correct answer is A. (8). Putting (q=3) gives \(\frac{27-3}{3}=8\). Simplify the numerator completely first.
Step 3
Exam Tip
(q=3) रखने पर \(\frac{27-3}{3}=8\) मिलता है। अंश को पहले पूरा सरल करें।
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(n) से शुरू होने वाली चार लगातार पूर्ण संख्याओं का योग क्या होगा?
What is the sum of four consecutive integers starting from (n)?
#algebraic_expressions
#hard
#consecutive_integers
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A (4n+6)
B (4n+4)
C (4n+10)
D (n+6)
Explanation opens after your attempt
Step 1
Concept
The four numbers are (n), (n+1), (n+2), and (n+3). Their sum is (4n+6).
Step 2
Why this answer is correct
The correct answer is A. (4n+6). The four numbers are (n), (n+1), (n+2), and (n+3). Their sum is (4n+6).
Step 3
Exam Tip
चार संख्याएं (n), (n+1), (n+2), (n+3) हैं। उनका योग (4n+6) है।
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व्यंजक (2(3x-4)-[x-2(1-x)]) का सरल रूप क्या है?
What is the simplified form of (2(3x-4)-[x-2(1-x)])?
#algebraic_expressions
#hard
#complex_brackets
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A (3x-6)
B (3x-10)
C (7x-6)
D (7x-10)
Explanation opens after your attempt
Step 1
Concept
Inside (x-2+2x=3x-2), so (6x-8-(3x-2)=3x-6). Simplify inside the square bracket first.
Step 2
Why this answer is correct
The correct answer is A. (3x-6). Inside (x-2+2x=3x-2), so (6x-8-(3x-2)=3x-6). Simplify inside the square bracket first.
Step 3
Exam Tip
अंदर (x-2+2x=3x-2), इसलिए (6x-8-(3x-2)=3x-6)। पहले वर्ग कोष्ठक के अंदर सरल करें।
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यदि (x=2) और (y=1), तो (2(x+y)2 -3xy) का मान क्या होगा?
If (x=2) and (y=1), what is the value of (2(x+y)2 -3xy)?
#algebraic_expressions
#hard
#evaluation_check
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A (12)
B (15)
C (18)
D (21)
Explanation opens after your attempt
Step 1
Concept
Substitution gives (2(3)2 -3(2)(1)=18-6=12). Evaluate brackets first.
Step 2
Why this answer is correct
The correct answer is B. (15). Substitution gives (2(3)2 -3(2)(1)=18-6=12). Evaluate brackets first.
Step 3
Exam Tip
मान रखने पर (2(3)2 -3(2)(1)=18-6=12) नहीं बल्कि (12) है। गणना में कोष्ठक पहले करें।
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यदि (x=2) और (y=1), तो (2(x+y)2 -3xy) का सही मान क्या है?
If (x=2) and (y=1), what is the correct value of (2(x+y)2 -3xy)?
#algebraic_expressions
#hard
#two_variable_square
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A (12)
B (15)
C (18)
D (21)
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Step 1
Concept
(2(x+y)2 -3xy=2(3)2 -3(2)(1)=18-6=12). Evaluate brackets and squares first.
Step 2
Why this answer is correct
The correct answer is A. (12). (2(x+y)2 -3xy=2(3)2 -3(2)(1)=18-6=12). Evaluate brackets and squares first.
Step 3
Exam Tip
(2(x+y)2 -3xy=2(3)2 -3(2)(1)=18-6=12)। कोष्ठक और वर्ग पहले निकालें।
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किस विकल्प में (2a-3b+5a+7b-4a) का सही सरल रूप है?
Which option gives the correct simplified form of (2a-3b+5a+7b-4a)?
#algebraic_expressions
#hard
#linear_terms
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A (3a+4b)
B (11a+4b)
C (3a-10b)
D (11a-10b)
Explanation opens after your attempt
Correct Answer
A. (3a+4b)
Step 1
Concept
(2a+5a-4a=3a) and (-3b+7b=4b). Combine only terms with the same variable.
Step 2
Why this answer is correct
The correct answer is A. (3a+4b). (2a+5a-4a=3a) and (-3b+7b=4b). Combine only terms with the same variable.
Step 3
Exam Tip
(2a+5a-4a=3a) और (-3b+7b=4b)। समान चर के पद ही मिलाएं।
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एक आयत की लंबाई (3x-2) और चौड़ाई (2x+5) है। परिमाप का व्यंजक क्या होगा?
A rectangle has length (3x-2) and breadth (2x+5). What is the expression for its perimeter?
#algebraic_expressions
#hard
#rectangle_perimeter
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A (10x+6)
B (5x+3)
C (10x+3)
D (5x+6)
Explanation opens after your attempt
Correct Answer
A. (10x+6)
Step 1
Concept
The perimeter is (2[(3x-2)+(2x+5)]=2(5x+3)=10x+6). Add length and breadth first.
Step 2
Why this answer is correct
The correct answer is A. (10x+6). The perimeter is (2[(3x-2)+(2x+5)]=2(5x+3)=10x+6). Add length and breadth first.
Step 3
Exam Tip
परिमाप (2[(3x-2)+(2x+5)]=2(5x+3)=10x+6) है। पहले लंबाई और चौड़ाई जोड़ें।
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यदि (x=1), तो \(4x^3-6x^2+5x-7\) का मान क्या होगा?
If (x=1), what is the value of \(4x^3-6x^2+5x-7\)?
#algebraic_expressions
#hard
#value_at_one
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A (-4)
B (-3)
C (3)
D (4)
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Step 1
Concept
Putting (x=1) gives (4-6+5-7=-4). Every positive power of (1) is (1).
Step 2
Why this answer is correct
The correct answer is A. (-4). Putting (x=1) gives (4-6+5-7=-4). Every positive power of (1) is (1).
Step 3
Exam Tip
(x=1) रखने पर (4-6+5-7=-4) मिलता है। (1) की हर धनात्मक घात (1) होती है।
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व्यंजक (5x-2[3x-{x+4}]) का सरल रूप क्या है?
What is the simplified form of (5x-2[3x-{x+4}])?
#algebraic_expressions
#hard
#braces_simplification
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A (x+8)
B (x-8)
C (9x+8)
D (9x-8)
Explanation opens after your attempt
Step 1
Concept
Inside (3x-(x+4)=2x-4), so (5x-2(2x-4)=x+8). Remove inner brackets first.
Step 2
Why this answer is correct
The correct answer is A. (x+8). Inside (3x-(x+4)=2x-4), so (5x-2(2x-4)=x+8). Remove inner brackets first.
Step 3
Exam Tip
अंदर (3x-(x+4)=2x-4), इसलिए (5x-2(2x-4)=x+8)। अंदरूनी कोष्ठक पहले हटाएं।
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किस विकल्प में \(3x^2-2x+7\) में से \(x^2+4x-5\) घटाने का सही परिणाम है?
Which option gives the correct result of subtracting \(x^2+4x-5\) from \(3x^2-2x+7\)?
#algebraic_expressions
#hard
#polynomial_subtraction
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A \(2x^2-6x+12\)
B \(4x^2+2x+2\)
C \(2x^2+2x+12\)
D \(4x^2-6x+2\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-6x+12\)
Step 1
Concept
(\(3x^2-2x+7\)-\(x^2+4x-5\)=2x-2 -6x+12). Change all signs of the second expression while subtracting.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-6x+12\). (\(3x^2-2x+7\)-\(x^2+4x-5\)=2x-2 -6x+12). Change all signs of the second expression while subtracting.
Step 3
Exam Tip
(\(3x^2-2x+7\)-\(x^2+4x-5\)=2x-2 -6x+12)। घटाते समय दूसरे व्यंजक के सभी चिह्न बदलें।
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